Regional Frequency Analysis of Annual Total Rainfall in Pakistan Using L-Moments


  • Ishfaq Ahmad International Islamic University, Islamabad
  • Aamir Abbas Department of Mathematics, Poonj University, Rawalakot, AJK, Pakistan
  • Muhammad Fawad International Islamic University, Islamabad
  • Aamir Saghir



Extreme events, L-Moments, Regional Frequency Analysis, Return periods, quantiles estimates


This study presents the estimation of regional quantiles of Annual Total Rainfall (ATR) for 30 meteorological stations using index flood procedure based on L-moments. Discordancy measure based on L-moments was used to screen the ATR. As a matter of the fact, highly elevated areas of Pakistan receive more rainfall, the study area was divided into four different regions. Further to justify the homogeneity of these regions, L-moment based heterogeneity measure (H) was calculated for each region using four parameter Kappa distribution. For each region, best distribution was found among Pearson type III (PE3), Generalized Normal (GNO), Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) distribution using Z-statistic and L-moment ratio diagram. Regional quantiles on the basis of best-fit distribution for each region
were determined and further for robustness, the accuracy measures for the estimated regional quantiles were calculated using Monte Carlo simulations. It was found that PE3 was the most suitable choice for large return period for first three regions while for small return period GNO and GEV. Similarly, for region IV GEV was declared as the best fit for lower return period’s up to 20 years while for a period of 50, 100, 500 and 1000 years GNO was the best one.

Author Biographies

Ishfaq Ahmad, International Islamic University, Islamabad

Assisistant Professor

Aamir Abbas, Department of Mathematics, Poonj University, Rawalakot, AJK, Pakistan


Muhammad Fawad, International Islamic University, Islamabad

MS student


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Engineering Sciences